If not been done, ask GP to check levels of vitamin d, b12, folate and ferratin. These all need to at good (not just average) levels for thyroid hormones (our own or replacement ones) to work in our cells
Make sure you get the actual figures from tests (including ranges - figures in brackets). You are entitled to copies of your own results.
When you get results suggest you make a new post on here and members can offer advice on any vitamin supplements needed
If you can not get GP to do these tests, then like many of us, you can get them done privately
Usual advice on ALL thyroid tests, (home one or on NHS) is to do early in morning, ideally before 9am. No food or drink beforehand (other than water) If you are taking Levo, then don't take it in 24 hours before (take straight after). This way your tests are always consistent, and it will show highest TSH, and as this is mainly all the medics decide dose on, best idea is to keep result as high as possible
You will see, time and time again on here lots of information and advice about importance of good levels of B12, folate, ferritin and vitamin D, leaky gut and gluten connection to autoimmune Hashimoto's & Grave's too.